Nonlinear Partial Differential Equations

Date: August 28, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Alexis Vasseur, University of Texas

Title: Nonlinear PDE Seminar

Abstract:

Title: The 3D Quasi-geostrophic equation: existence of solutions, lateral boundary conditions and regularity.

Abstract:
The 3D Quasi-geostropic equation is a model used in climatology to model the evolution of the atmosphere for small Rossby numbers. It can be derived from the primitive equation. The surface quasi-geostrophic equation (SQG) is a special case where the atmosphere above the earth is at rest. The evolution then depends only on the boundary condition, and can be reduced to a 2D model.
In this talk, we will show how we can derive the physical lateral boundary conditions for the inviscid 3D QG, and construct global in time weak solutions. Finally, we will discuss the global regularity of solutions to the QG equation with Ekman pumping.